Problem: Rewrite as a simplified fraction. ${3.\overline{91} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 391.9191...\\ 1x &= 3.9191...\end{align*}}$ Subtracting the two equations, we have: ${99x = 388}$ ${x = \dfrac{388}{99}} \text{or} {3 \dfrac{91}{99}}$